Convergence of the hyperspherical adiabatic expansion for helium-like systems

Abstract

The convergence of the hyperspherical adiabatic expansion for helium-like systems has been studied numerically. The spectral problems arising after approximate separation of variables are solved by the finite-difference and finite-element methods. The energies of the ground and some doubly excited states of the negative hydrogen ion are calculated in the six-channel approximation within 10-4 au accuracy. The results obtained demonstrate a rapid convergence of the hyperspherical adiabatic expansion and agree reasonably well with experimental data as well as with other more complicated theoretical calculations.